An optical frequency comb is an optical spectrum of equidistant lines. The use of frequency combs as a tool may depend on the spacing between teeth (lines) of the comb. Mode-locked lasers can provide accurate frequency combs. A mode-locked laser produces a stream of identical pulses, which can have a duration of only several femtoseconds, at a repetition rate typically in the range of 70 to 150 MHz. In the frequency domain, the laser output consists of a frequency comb having equidistant lines. Because these lines are exactly equally spaced, this frequency comb can be used as a ruler for optical frequencies. Given an atomic line (frequency standard) as reference, this ruler can be used, in principle, to determine with absolute accuracy and high precision the optical frequency of any optical source, by comparing (beating) the frequency of that source with the closest line of the ruler, and counting the teeth (lines) of the comb that span the difference between the frequency standard and the unknown source. For this type of measurement to be practical, there should be line indicators (“tickmarks”) spaced by much more than the typical 100 MHz of a Ti:sapphire mode locked laser, similar to a ruler for length measurements, for example, in which there are different tickmarks for 1 mm, 1 cm, 10 cm, and 1 m. The need for such instrumentation having tickmarks ranges from measurements of atomic lines and physical constants to accurate monitoring of spectral lines in astronomy.
There have been various attempts to increase tooth spacing. In the articles “Fabry-Perot filter cavities for wide-spaced frequency combs with large spectral bandwidth;” T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. H{umlaut over ( )}ansch, and T. Udem; Applied Physics B: Lasers and Optics, 96:251-256, 2009 and “Multiplying the repetition rate of passive mode-locked femtosecond lasers by an intracavity flat surface with low reflectivity;” T. M. Liu, F. X. Kartner, J. G. Fujimoto, and C. K. Sun. Optics letters, 30:439-441, 2005, a proposed method to increase tooth spacing has included the use of a Fabry-Perot cavity to multiplex the pulse train from a mode-locked laser. The shortcomings of this method are threefold. First, because the device is passive, the average power is reduced. Additional amplification may be required. Second, because of the unavoidable cavity dispersion, the unequal spacing of the Fabry-Perot modes defeats the purpose of a comb of absolute accuracy. Even when the cavity is in vacuum, there will be dispersion due to the mirror coatings. Finally, matching the carrier-to envelope offset (CEO) of the driving laser and slave cavity requires sophisticated stabilization methods. The CEO is the tooth frequency of the (extended) comb closest to zero frequency. Equivalently, it is also the change in carrier phase (with respect to the envelope) from pulse to pulse, divided by the time between two successive pulses. The CEO is an important parameter of pulse trains related to the change in phase from pulse to pulse in the train.
Another approach has included the use of the properties of the mode-locked laser in making combs of perfect spacing by combining a driving laser with a slave laser, (rather than passive) cavity. In another approach as discussed in the article by Liu et al. mentioned above, the insertion of a low reflectivity (4%) interface inside a mode-locked laser cavity to multiplex its repetition rate has been proposed. However, such an approach may be difficult, as the alignment of the reflecting face is extremely critical (it has to be perfectly parallel to the output coupler), and its position has to be located at an exact fraction of the cavity length.